```{r data generation, echo = FALSE, results = "hide"}
## parameters
a <- sample(2:9, 1)
b <- sample(2:4, 1)/10
c <- sample(6:9, 1)/10
## solution
res <- exp(b * c) * (a * c^(a-1) + b * c^a)
```

Question
========
What is the derivative of $f(x) = x^{`r a`} e^{`r b` x}$, evaluated at $x = `r c`$?

Solution
========
Using the product rule we obtain
$$ f'(x) = e^{`r b` x} \cdot (`r a` \cdot x^`r a-1` + `r b` x^`r a`). $$
Evaluated at $x = `r c`$ and rounded to two digits the answer is
$f'(`r c`) = `r fmt(res, 6)` = `r fmt(res, 2)`$.

Meta-information
================
extype: num
exsolution: `r fmt(res, 2)`
exname: exp derivative
extol: 0.01
